(4n-3)(2n+1)=63

Solution for (4n-3)(2n+1)=63 equation:

Simplifying
(4n + -3)(2n + 1) = 63

Reorder the terms:
(-3 + 4n)(2n + 1) = 63

Reorder the terms:
(-3 + 4n)(1 + 2n) = 63

Multiply (-3 + 4n) * (1 + 2n)
(-3(1 + 2n) + 4n * (1 + 2n)) = 63
((1 * -3 + 2n * -3) + 4n * (1 + 2n)) = 63
((-3 + -6n) + 4n * (1 + 2n)) = 63
(-3 + -6n + (1 * 4n + 2n * 4n)) = 63
(-3 + -6n + (4n + 8n2)) = 63

Combine like terms: -6n + 4n = -2n
(-3 + -2n + 8n2) = 63

Solving
-3 + -2n + 8n2 = 63

Solving for variable 'n'.

Reorder the terms:
-3 + -63 + -2n + 8n2 = 63 + -63

Combine like terms: -3 + -63 = -66
-66 + -2n + 8n2 = 63 + -63

Combine like terms: 63 + -63 = 0
-66 + -2n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + -1n + 4n2) = 0

Factor a trinomial.
2((-11 + -4n)(3 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + -4n)' equal to zero and attempt to solve:

Simplifying
-11 + -4n = 0

Solving
-11 + -4n = 0

Move all terms containing n to the left, all other terms to the right.

Add '11' to each side of the equation.
-11 + 11 + -4n = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -4n = 0 + 11
-4n = 0 + 11

Combine like terms: 0 + 11 = 11
-4n = 11

Divide each side by '-4'.
n = -2.75

Simplifying
n = -2.75
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-2.75, 3}